4(7+5x^2)=340

Solution for 4(7+5x^2)=340 equation:

4(7+5x^2)=340

We move all terms to the left:

4(7+5x^2)-(340)=0

We multiply parentheses

20x^2+28-340=0

We add all the numbers together, and all the variables

20x^2-312=0

a = 20; b = 0; c = -312;
Δ = b2-4ac
Δ = 02-4·20·(-312)
Δ = 24960
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24960}=\sqrt{64*390}=\sqrt{64}*\sqrt{390}=8\sqrt{390}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{390}}{2*20}=\frac{0-8\sqrt{390}}{40}
=-\frac{8\sqrt{390}}{40}
=-\frac{\sqrt{390}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{390}}{2*20}=\frac{0+8\sqrt{390}}{40}
=\frac{8\sqrt{390}}{40}
=\frac{\sqrt{390}}{5}
$